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arXiv:1804.10725 · Physical review. B./Physical review. B

Quench dynamics across topological quantum phase transitions

Shiuan-Fan Liou, Kun Yang

Published Jun 25, 2018• 24 citations
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Abstract

We study the dynamics of systems quenched through topological quantum phase transitions and investigate the behavior of the bulk and edge excitations with various quench rates. Specifically, we consider the Haldane model and checkerboard model in slow quench processes with distinct band-touching structures leading to topology changes. The generation of bulk excitations is found to obey the power-law relation Kibble-Zurek and Landau-Zener theories predict. However, an anti-Kibble-Zurek behavior is observed in the edge excitations. The mechanism of excitation generation on edge states is revealed, which explains the anti-Kibble-Zurek behavior.

DOI
10.1103/physrevb.97.235144

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We study the dynamics of systems quenched through topological quantum phase transitions and investigate the behavior of the bulk and edge excitations with various quench rates. Specifically, we consider the Haldane model and checkerboard model in slow quench processes with distinct band-touching structures leading to topology changes. The generation of bulk excitations is found to obey the power-law relation Kibble-Zurek and Landau-Zener theories predict. However, an anti-Kibble-Zurek behavior is observed in the edge excitations. The mechanism of excitation generation on edge states is revealed, which explains the anti-Kibble-Zurek behavior.
We study the quantum quench of a finite rate across topological quantum transitions in two-dimensional Chern and Z2{Z}_{2}Z2​ topological insulators. We choose the representative Haldane model and the Kane-Mele model to investigate the behavior of excitation density generated by the quench and the impact of disorder on it. For the Haldane model, as long as the spectral gap is not closed by disorder, we find the excitation density at the end of the quench obeys the power-law decay with decreasing quench rate, and the power is consistent with the prediction of the Kibble-Zurek mechanism. By contrast, the Kibble-Zurek scaling of excitation density is absent in the Kane-Mele model once disorder is switched on, which we attribute to the emergence of a disorder-induced gapless region. In particular, the anti-Kibble-Zurek behavior of excitation density, namely, larger excitation density at slower quench, is observed at suitable model parameters. Moreover, we demonstrate that particle's onsite occupation can be used as a local measurable quantity to probe the breakdown of adiabatic evolution. The difference of onsite occupation between the time-evolved state and the instantaneous ground state at the end of the quench can successfully capture the key features of excitation density for both the Haldane and Kane-Mele models under periodic and more realistic open boundary conditions, thus facilitating the experimental characterization of the quench dynamics in these models.
We study the nonadiabatic dynamics of a two-dimensional higher-order topological insulator when the system is slowly quenched across the boundary-obstructed phase transition, which is characterized by edge band gap closing. We find that the number of excitations produced after the quench exhibits power-law scaling behaviors with the quench rate. Boundary conditions can drastically modify the scaling behaviors: The scaling exponent is found to be α=1/2α=1/2α=1/2 for hybridized and fully open boundary conditions, and α=2α=2α=2 for periodic boundary condition. We argue that the exponent α=1/2α=1/2α=1/2 cannot be explained by the Kibble-Zurek mechanism unless we adopt an effective dimension deff=1d^{\rm eff}=1deff=1 instead of the real dimension d=2d=2d=2. For comparison, we also investigate the slow quench dynamics across the bulk-obstructed phase transitions and a single multicritical point, which obeys the Kibble-Zurek mechanism with dimension d=2d=2d=2.
The Kibble-Zurek mechanism predicts a universal scaling behavior of the defect production when a system is slowly quenched across a critical phase transition point. Here, we discover that the universal scaling behavior across a higher-order topological phase transition does not conform to the traditional Kibble-Zurek mechanism. To explain the anomalous scaling exponent, we develop a solvable Landau-Zener model that takes into account the role of topological edge band that dominates the phase transition. For a two-dimensional boundary-obstructed higher-order topological system, the Kibble-Zurek scaling must be modified to adopt the effective dimension of topological edge band instead of the real physical dimension. We also find that across the boundary-obstructed higher-order topological phase transition, boundary conditions can drastically modify the scaling behaviors. For comparison, we investigate the slow quench dynamics across the bulk-obstructed phase transitions and a single multicritical point, which obeys the Kibble-Zurek mechanism with physical dimension.
The Kibble-Zurek (KZ) mechanism renders a theoretical framework for elucidating the formation of topological defects across continuous phase transitions. Nevertheless, it is not immediately clear whether the KZ mechanism applies to topological phase transitions. The direct experimental study for such a topic is hindered by quenching a certain parameter over orders of magnitude in topological materials. Instead, we investigate the KZ behavior across topological transitions of a Chern band in two-dimensional (2D) optical Raman lattices with quantum gases. Defined as the defects, excitation density is reconstructed via measuring the spin wave functions, with which the power-law scaling of total excitation density is extracted and such scaling could be interpreted within the KZ framework. Our work has heralded the commencement of experimentally exploring the KZ mechanism of the topological phase transitions.
When a system is driven across a continuous phase transition, the density of topological defects demonstrates a power-law scaling behavior versus the quenching rate, as predicted by Kibble-Zurek mechanism. In this study, we generalized this idea and address the scaling of quantum state transport in a one-dimensional topological system subject to a linear drive through its topological quantum phase transition point. We illustrate the power-law dependencies of the quantum state's transport distance, width, and peak magnitude on the driving velocity. Crucially, the power-law exponents are distinct for the edge state and bulk state. Our results offer a novel perspective on quantum state transfer and enriches the field of Kibble-Zurek behaviors and nonadiabatic quantum dynamics.
When a system is driven across a continuous phase transition, the density of topological defects demonstrates a power-law scaling behavior versus the quenching rate, as predicted by the Kibble-Zurek mechanism. In this study, we generalize this idea and address the scaling of quantum state transport in a one-dimensional topological system subject to a linear drive through its topological quantum phase transition point. We illustrate the power-law dependences of the quantum state's transport distance, width, and peak magnitude on the driving velocity. Crucially, the power-law exponents are distinct for the edge state and bulk state. Our results offer a different perspective on quantum state transfer and enrich the field of Kibble-Zurek behaviors and nonadiabatic quantum dynamics.